Tooth modeling system

ABSTRACT

Systems and methods are disclosed for treating teeth to correct for malocclusions. This may be accomplished by applying a series of labels to a digital dental model and applying a rolling ball process to identify tooth boundaries separating one tooth from a neighboring tooth and to also determine the crown/gum margin. The user may further assign regions to the dental model to indicate hard regions and soft regions. With the dental model labeled and defined, the user may then generate a treatment plan for moving the labeled and defined tooth or teeth relative to one another to correct for any malocclusions. Upon approval of the treatment plan, a series of 3D printed dental appliances or aligners to be worn in series by the patient may be fabricated to ultimately move the tooth or teeth to a desired position.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 15/230,139 filed Aug. 5, 2018 (now U.S. Pat. No. 10,624,717), which claims the benefit of priority to U.S. Provisional Application No. 62/238,554 filed Oct. 7, 2015, which are incorporated herein by reference in their entireties.

FIELD OF THE INVENTION

The present invention relates to methods and apparatus for computerized orthodontics. More particularly, the present invention relates to methods and apparatus for planning orthodontic treatments.

BACKGROUND OF THE INVENTION

Orthodontics is a specialty of dentistry that is concerned with the study and treatment of malocclusions which can result from tooth irregularities, disproportionate facial skeleton relationships, or both. Orthodontics treats malocclusion through the displacement of teeth via bony remodeling and control and modification of facial growth.

This process has been traditionally accomplished by using static mechanical force to induce bone remodeling, thereby enabling teeth to move. In this approach, braces having an archwire interface with brackets are affixed to each tooth. As the teeth respond to the pressure applied via the archwire by shifting their positions, the wires are again tightened to apply additional pressure. This widely accepted approach to treating malocclusions takes about twenty-four months on average to complete, and is used to treat a number of different classifications of clinical malocclusion. Treatment with braces is complicated by the fact that it is uncomfortable and/or painful for patients, and the orthodontic appliances are perceived as unaesthetic, all of which creates considerable resistance to use. Further, the treatment time cannot be shortened by increasing the force, because too high a force results in root resorption, as well as being more painful. The average treatment time of twenty-four months is very long, and further reduces usage. In fact, some estimates provide that less than half of the patients who could benefit from such treatment elect to pursue orthodontics.

Kesling introduced the tooth positioning appliance in 1945 as a method of refining the final stage of orthodontic finishing after removal of the braces (debanding). The positioner was a one-piece pliable rubber appliance fabricated on the idealized wax set-ups for patients whose basic treatment was complete. Kesling also predicted that certain major tooth movements could also be accomplished with a series of positioners fabricated from sequential tooth movements on the set-up as the treatment progressed. However, this idea did not become practical until the advent of three-dimensional (3D) scanning and use of computers by companies including Align Technologies and as well as OrthoClear, ClearAligner, and ClearCorrect to provide greatly improved aesthetics since the devices are transparent.

However for traditional trim model to individual tooth, the gum geometry is lost and the fake gum is recreated, often remodeled by a technician. Hence, the gum geometry may not be accurate at first and an animation of gum changes over time due to lack of a physical model is even harder to model. Such inaccurate modeling causes the resulting aligner to be mismatched resulting in devices which are too large or too small resulting in patient discomfort.

Another problem is that without the real gum as the reference, some so-called modeled treatments cannot be achieved in reality resulting in potential errors, e.g., a tooth movement can occur within a mis-modeled gingival, however, the tooth movement may actually be moved exteriorly of a patient's real gingival.

Another problem of trimming and hole filling and creating an individual tooth and gum model is there is little information that can define the real boundary of two teeth. Such trim and fill models force the boundary surfaces to be defined even if they are arbitrary.

Depending on what boundary surface is defined, the movement can be restricted or relax, meaning some real life movement can be achieved; however, due to such inaccuracies, the modeling software is unable to model accurately due to models colliding into each other. This may cause the real treatment outcome to create gaps between teeth and further requiring final refinements which increase cost and patient dissatisfaction. On the other hand, if the modeled movement is relax, the software may enable movements which are physically impossible in reality and this may cause the modeled device to push teeth into one another unable to move. This may also cause the plastic shell of the aligner to sometimes stretch so much that the shell applies an uncomfortable amount of force, which could be painful, to a patient.

Another problem of trim and hole fill is the filling of the geometry like a real tooth, for below, the below lines are likely of boundary surfaces modeled, such models look like a real tooth; however, such sharp boundaries cause deeper undercuts which, once printed and thermal formed to have a plastic shell, make removal of the plastic shell from the printed model difficult due to the deep undercuts. To compensate for this, a bevel object is typcially created to fill the clevis increasing inaccuracy and costs.

Another problem of trim and hole filling is the model size is too large to communicate between the user and manufacturer thus requiring that the model size be reduced resulting in missing model details. These inaccuracies could misguide professionals, e.g., the full complex model may not show a gap between two adjacent teeth however the reduced model may show one.

These 3D scanning and computerized planning treatments are cumbersome and time consuming. Accordingly, there exists a need for an efficient and cost effective procedure for planning the orthodontic treatment of a patient.

SUMMARY OF THE INVENTION

Systems and methods are disclosed for treating teeth to correct for malocclusions. This may be accomplished by applying a series of labels to a digital dental model and applying a rolling ball process to identify tooth boundaries separating one tooth from a neighboring tooth. The rolling ball process may also be used to determine the crown/gum margin. The user may further assign regions to the dental model to indicate hard regions (hard regions have a criteria where they cannot change their shape) and soft regions (soft regions have a criteria where they can deform with an attached hard region). With the dental model labeled and defined, the user may then generate a treatment plan for moving the labeled and defined tooth or teeth relative to one another to correct for any malocclusions. Upon approval of the treatment plan, a series of 3D printed dental appliances or aligners to be worn in series by the patient may be fabricated to ultimately move the tooth or teeth to a desired position.

One method for planning a treatment for correcting malocclusions may generally comprise receiving a scanned dental model of a subject's dentition and then applying a label to one or more teeth within the dental model. The rolling ball process may be simulated along an exterior of the one or more teeth and gums within the dental model for determining a boundary between each of the one or more teeth and gums based on a path or trajectory of the rolling ball process. The hard or soft regions may be assigned to each of the one or more teeth and gums within the dental model and a position of the one or more teeth within the dental model may be moved by the user to correct for malocclusions in developing a treatment plan. Once approved (e.g., by the patient and/or user), one or more prostheses or aligners may be fabricated to move the one or more teeth according to the treatment plan.

Moving a position of the one or more teeth in developing the treatment plan generally comprises morphing a new dental model from the dental model. As described, the one or more prostheses or aligners may be fabricated, e.g., via 3D printing the one or more aligners, so that the entire process of may be accomplished in a single visit by the subject to a dental office.

In another example for planning a treatment for correcting malocclusions, the method may generally comprise directly scanning a subject's dentition to create a digitized dental model and having the user apply a label to one or more teeth within the dental model. The simulated ball may be rolled digitally along an exterior of the one or more teeth and gums within the dental model for determining a boundary between each of the one or more teeth and gums based on a path or trajectory of the rolling ball process. The hard region may be assigned to each of the one or more teeth and a soft region may be similarly assigned to gums within the dental model. Then a position of the one or more teeth may be moved within the dental model to correct for malocclusions in developing a treatment plan.

As described, once the treatment plan has been approved (e.g., by the patient and/or user), one or more prostheses or aligners may be fabricated to move the one or more teeth according to the treatment plan and the entire process of may be accomplished in a single visit by the subject to a dental office.

Advantages of the system may include one or more of the following. The system allows close control by the treating professional at each stage by allowing specific movements from one stage to the next stage. In one example, it is desirable in some settings to synchronize the movement and operation of the individual tooth models to have a few tooth models operate in a choreographed manner as dictated by a treating professional. Having this choreographed movement is not typically possible through manual control where the tooth models move randomly and independently. The present control method and/or system are ideal for use in moving a number of tooth models and to provide synchronized tooth movement. Such a method may be non-swarming to avoid any collisions between the teeth and to also avoid the appearance of merely random movements, at least in some applications. Rather, it is desirable for the tooth models to each react safely to environmental conditions such as changes in bone structure and soft tissue during group tooth movement of choreographed tooth models.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a flow diagram of one exemplary method for a tooth modeling system.

FIG. 1B shows another exemplary method for adjusting a treatment process when results deviate from the initial treatment plan.

FIG. 2 shows one exemplary process for planning a treatment process in creating a model file.

FIG. 3 shows one exemplary labeling system in planning the treatment process.

FIG. 4 shows a rolling or dropping ball method for detecting the tooth boundary during treatment planning.

FIG. 5A shows how the rolling or dropping ball follows the clevis of teeth.

FIG. 5B shows how the ball trajectory path can be used to find the margin lines between adjacent teeth.

FIG. 5C show how once the margins are defined, the entire dental model may be separated into two portions to detect a tooth boundary or geometry.

FIG. 6 shows an exemplary mass-spring model which may be used to model the teeth and gums as an interconnected system.

FIG. 7 shows an example of how the treatment planning may be implemented with respect to the patient.

DETAILED DESCRIPTION OF THE INVENTION

The present invention will be described with respect to particular embodiments but the invention is not limited thereto but only by the claims. Any reference signs in the claims shall not be construed as limiting the scope thereof.

As used herein, the singular forms “a”, “an”, and “the” include both singular and plural referents unless the context clearly dictates otherwise.

The terms “comprising”, “comprises” and “comprised of” as used herein are synonymous with “including”, “includes” or “containing”, “contains”, and are inclusive or open-ended and do not exclude additional, non-recited members, elements or method steps. The terms “comprising”, “comprises” and “comprised of” when referring to recited members, elements or method steps also include embodiments which “consist of” said recited members, elements or method steps.

Furthermore, the terms first, second, third and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequential or chronological order, unless specified. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

The term “about” as used herein when referring to a measurable value such as a parameter, an amount, a temporal duration, and the like, is meant to encompass variations of +/−10% or less, preferably +/−5% or less, more preferably +/−1% or less, and still more preferably +/−0.1% or less of and from the specified value, insofar such variations are appropriate to perform in the disclosed invention. It is to be understood that the value to which the modifier “about” refers is itself also specifically, and preferably, disclosed.

The recitation of numerical ranges by endpoints includes all numbers and fractions subsumed within the respective ranges, as well as the recited endpoints.

All documents cited in the present specification are hereby incorporated by reference in their entirety.

Unless otherwise defined, all terms used in disclosing the invention, including technical and scientific terms, have the meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. By means of further guidance, definitions for the terms used in the description are included to better appreciate the teaching of the present invention. The terms or definitions used herein are provided solely to aid in the understanding of the invention.

Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to a person skilled in the art from this disclosure, in one or more embodiments. Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

The treatment planning process may be implemented after receiving and analyzing the scanned dental model of a patient's dentition. The scanned dental model may be accordingly processed to enable the development of a treatment plan which can be readily implemented for fabricating one or more positioners for use in effecting sequential tooth movements.

FIG. 1A shows an exemplary overall tooth modeling process which may be used in planning the treatment for correcting malocclusions in a patient. The process shown may involve initially acquiring a patient's dental record 110 in the form of, e.g., lower arch and/or upper arch CAD files, intra oral photos, X-rays or 3D CT scans, etc. The lower arch and/or upper arch CAD files may be created, for instance, through a number of different methods, such as taking lower and upper impressions of the patient's dentition, X-rays, etc.

Once the dental records are acquired, the lower arch and upper arch relationship may be imported or calculated 112 for registration by one or more computing devices and a flexible dental anatomy model may be auto created 114 by one or more processors located locally in proximity to where the patient is treated, e.g., dental office, or remotely from the patient location. Once the dental anatomy model has been digitally created and confirmed to fit and that the arch model can open and close as expected, one or more possible treatments may be created in real-time chairside of the patient 116 and the one or more treatment options may be may be shown and/or discussed with the patient chairside 118 where simulations of the treatment options may also be shown and/or discussed for potentially altering the treatment plan as needed. The simulations of treatment options may be displayed to the patient using any number of electronic display methods.

Following the discussion of the treatment options with the patient, the treatment plan (with any alterations) may be used to generate manufacturing files for the fabrication machinery 120, e.g., 3D printing machines, thermal forming, laser sintering, etc. Because the resulting one or more positioners may be fabricated locally in proximity to the patient (e.g., dental office, clinic, nearby facility, etc.) the one or more resulting positioners for use by the patient may be fabricated locally allowing for the patient to try on the one or more positioners 122 during the same visit.

Such a treatment plan may have particular advantages over conventional planning and treatment plans including one or more of the following:

-   -   exact treatment may be developed right way and discussed with         the patient in real time;     -   practitioner has full control of the treatment plan options         which are easy to create;     -   real gum modeling may be implemented;     -   one or more positioners may be fabricated locally allowing the         patient to try-on during the same visit;     -   easy to incorporate other treatment methods, e.g. indirect         bonding bracket, rubber bands, hooks, retainers, etc. in         combination with one or more positioners.

Even in the event that a treatment plan has been developed and implemented for a patient, as shown and described for FIG. 1A, the actual progress of the tooth movement(s) may not correspond to the treatment plan or the actual progress may begin to deviate from the treatment plan. Because of this variability, not all of the positioners or aligners may be fabricated at the start of the treatment but the positioners may instead be fabricated in preset stages for use by the patient until a subsequent visit to the practitioner, e.g., every six weeks, where a new set of positioners may be fabricated for subsequent treatments. FIG. 1B shows an example of this staged treatment planning where the treatment plan may be adjusted during the actual treatment according to any changes or deviations by the patient's progress. Furthermore, the implementation of a staged treatment planning process also enables the practitioner to employ other devices or methods (e.g., brackets, wires, etc.) for correcting malocclusions in addition to or in place of the fabricated positioners.

As described above, the patient's dentition may be scanned or otherwise recorded to capture a three-dimensional (3D) representation 130 of the patient's dentition and an initial treatment plan may be determined 132 for forming one or more dental appliances 134 for correcting any malocclusions. Rather than fabricating the dental appliances for the entire treatment process, a staged number of appliances may be initially fabricated for use by the patient until their subsequent visit. The practitioner may evaluate the patient's tooth movement progress at subsequent visits according to the treatment plan 136 as originally developed. In determining whether the patient's tooth movement progress differs from the treatment plan 138, the practitioner may compare the treatment plan with the patient's actual tooth movement(s) to determine whether they correlate with one another. Such a comparison may be done in a number of ways, e.g., visually by the practitioner or the patient's dentition may be scanned again and the captured 3D representation of the treated dentition may be digitally compared against the treatment plan.

If the system determines that the actual tooth movement progress does not differ from the treatment plan, the tooth movement may be continued according to the treatment plan 140 without alteration and an additional number of positioners may be fabricated for use by the patient until the subsequent visit. Provided that the next visit and subsequent visit tracks according to the original treatment plan, the additional set of positioners may be fabricated until the treatment has been completed and the malocclusions corrected.

However, if during any one of the evaluations the practitioner determines that the actual tooth movement does differ from the treatment plan, the practitioner may be alerted of the deviation 142 by the system. The treatment plan may then be automatically adjusted by the system for the next set of dental appliances or positioners 144 to correct for the deviations so that the newly fabricated positioners provide for a better fit to the patient's dentition and is responsive to correcting for the deviations. At subsequent visits, the tooth movement with the altered treatment plan may be evaluated 136 to determine whether the tooth movement differs from the altered treatment plan 138 and if no deviation is detected, treatment may be continued but if a deviation is detected, the practitioner may be alerted of the deviation and the altered treatment plan again be adjusted accordingly. This process may be continued until the detected tooth movements appear to follow the treatment plans.

Because the system is programmed to alert the practitioner of any deviations for particular teeth, the practitioner is able to determine if the patient is non-compliant with wearing the positioner and/or whether any there are any problematic tooth movements which the practitioner can then flag for continuing treatment or whether other devices or methods, e.g., conventional braces, may be employed for particularly problematic teeth. The treatment plan (as any subsequent treatment plans) may be shared with others through any number of methods and/or devices.

In importing or calculating the relationship between the lower arch and upper arch 112, the digital models of the lower arch and/or upper arch may be loaded 150, e.g., into a computer, as shown in the flow diagram of FIG. 2 . Additionally, as part of creating a dental anatomy model 114, the bite registration between the lower arch and upper arch may be set and mounted on a virtual articulator 152 and the user may then drag and drop the tooth ID to an area of interest 154 for correcting the malocclusion. In digitally modeling the margin between the crown and gum, the process may assign regions that are designated as “hard” and “soft” 156 with conditions set where a region with a “hard” designation cannot change its shape and a region with a “soft” designation is able to be deformed with an attached “hard” region.

Additionally, any number of moving widgets may be defined at various regions or locations 158 for facilitating the movement and control of the regions. For instance, the process may allow for defining moving widgets: mesial/distal, lingual/facial, vertical, etc. Moreover, the user may be enabled to control the widgets and calculate a morphed new model 160 in developing a treatment plan. Once the treatment plan has been completed, the plan may be exported, e.g., to a 3D printer acceptable model file 162, for use in manufacturing one or more of the positioners or for manufacturing molds for subsequent thermal forming.

In preparing the scanned image of the patient's dentition for treatment planning, the digital model may be initially labeled. For example, FIG. 3 shows an example of a labeling system where the scanned dentition model 170 may be seen. A number of labels 172, in this example a total of 16 labels (e.g., 1 to 16 or 17-32 depending on the arch), may be initially laid out alongside the model 170 allowing for the user to assign a label to a targeted tooth by, e.g., dragging and dropping a label to a particular tooth. In this example, while the label is dragged it may remain visible but after being assigned by being dropped upon a particular tooth, the tooth may change to indicate that it has been labeled. For instance, the tooth may be changed in color to indicate that it is now labeled, e.g., from the color red to indicate an unassigned tooth to the color white to indicate the tooth being labeled.

In facilitating the treatment planning, moving widgets may be defined on the digital model 158 and controlled 160 accordingly, as discussed above. As shown in FIG. 3 , one example is illustrated of a moving widget where a center vertex 174 indicated as a circle may be defined along the model 170. The selected vertex related mesh should be form a single connected region to provide a way to read the list. The center vertex 174 is indicated as a center while a second vertex 176 may be defined relative to the center vertex 174 such that the first arm 178 defined between may point directly outside the tooth surface in the lingual to buccal direction. A third vertex 180 may be defined relative to the center vertex 174 such that the second arm 182 defined between points along the center of the teeth in the mesial to distal direction. The first arm 178 and second arm 182 need not be perpendicular to one another. The moving widget may be applied only to teeth which are labeled (and hence teeth which may be moved in the model) and may provide a way to read and orient the direction of the arms 178, 182 and their origin. The moving widget may be hidden from view from the user when not in use.

Once the tooth labeled and a small set of mesh are identified, a drop ball algorithm may be used to detect the gum margin and teeth margin. FIG. 4 shows an exemplary process for digitally detecting and identifying a tooth boundary or geometry from the scanned dentition of the patient by simulating a rolling or dropping ball 194 to detect the boundary of the tooth 190 and gum 192. The ball 194 may be simulated to roll from a high energy state 196, e.g., at the tooth crown, to a low resting state 198, e.g., at bottom of the tooth. As the ball 194′ rolls down longitude, there is a bump 200 which tip up at the margin area between the tooth and gum where the inflection changes. By looking at these areas and at the correct curvature changes, the margin line can be detected. This method can also detect occlusal teeth margins and gum margins as well.

However, to detect the side margin between two adjacent teeth, the rolling ball algorithm may be used, as described, to follow the known margin lines of the teeth but in-between the adjacent teeth, the boundary of the teeth may be extrapolated. For instance, FIG. 5A shows an example where the rolling ball 194 may be rolled to follow the outline of adjacent teeth 212, 214. The region 218 in-between the teeth may be generally inaccessible to the ball 194 but the ball will naturally follow the clevis 216 of the teeth. Hence, the extrapolated trajectory path 220, 222 that the rolling ball 194 would follow between the teeth 212, 214 can be used to find the margin lines between adjacent teeth 212, 214 even though the ball 194 may not access the region 218 in-between, as illustrated in FIG. 5B.

As shown in FIG. 5C, once the margins are defined over the model, the entire dental model may be separated into two parts: a hard crown surface and a soft gum surface. In one embodiment, the “hard” surface 224, 226 may be considered a rigid surface which moves in an integral part and maintains its shape whiling moving. The “soft” surface 228, 230 may be attached to the “hard” surface 224, 226 and may deform based on the movements of the hard surface 224, 226. Such a movement does not change the overall topological structure of the dental model, hence the finished model by default is watertight, which fits a 3D printer requirement.

This deviates from the traditional separate model to individual tooth model, which requires models to be trimmed and then capped (hole filling) to make it watertight. Due to the complexity of scanned tooth geometry, such trim and hole filling is a very complex process.

FIG. 6 shows an exemplary mass-spring model 240 which may be applied to the dental model in determining tooth movement. It is generally desirable in some settings to synchronize the movement and operation of the individual tooth models to have a few tooth models operate in a choreographed manner as dictated by a treating professional. Having this choreographed movement is not typically possible through manual control where the tooth models move randomly and independently. The present control method and/or system are ideal for use in moving a number of tooth models and to provide synchronized tooth movement. Such a method may be non-swarming to avoid any collisions between the teeth and to also avoid the appearance of merely random movements, at least in some applications. Rather, it is desirable for the tooth models to each react safely to environmental conditions such as changes in bone structure and soft tissue during group tooth movement of choreographed tooth models.

The mass-spring model 240 may be constrained to be directly attached to a hard surface and the model 240 can be stretched or compressed. Any number of algorithms can be used to calculate its shape, e.g. mass-spring model, in one implementation of mass-spring model 240, two nodes may be modeled as mass points connected by a parallel circuit of a spring and a damper. In this approach, the body is modeled as a set of point masses (nodes) connected by ideal weightless elastic springs obeying some variant of Hooke's law. These nodes may either derive from the edges of a two-dimensional polygonal mesh representation of the surface of the object, or from a three-dimensional network of nodes and edges modeling the internal structure of the object (or even a one-dimensional system of links, if for example a rope or hair strand is being simulated). Additional springs between nodes can be added, or the force law of the springs modified, to achieve desired effects. Having the dental model constrained as a mass-spring model 240 helps to synchronize the movement and operation of the individual tooth models to have a few tooth models operate in a choreographed manner.

Applying Newton's second law to the point masses including the forces applied by the springs and any external forces (due to contact, gravity, etc.) gives a system of differential equations for the motion of the nodes, which is solved by standard numerical schemes for solving ordinary differential equations. Rendering of a three-dimensional mass-spring lattice is often done using free-form deformation, in which the rendered mesh is embedded in the lattice and distorted to conform to the shape of the lattice as it evolves. Assuming all point masses equal to zero, one can obtain the stretched grid method aimed at several engineering problems solution relative to the elastic grid behavior.

Another way to calculate the model 240 is using finite element analysis (FEA) models where the “soft” parts of the model are separated into smaller FEA elements, e.g., tetrahedron or cube elements, and some of the element surfaces may be attached to “hard” portions as so called boundary condition in FEA analysis while “soft” portions (gum portions) may be assigned various material properties such as Young's Modulus consistent with gum portions. While the hard parts are moving, the boundary condition may change and hence all the elements based on its connections to its neighboring elements may form a large matrices. By solving such matrices, each individual element shape and locations may be calculated to give a calculated gum deformation during treatment.

In one embodiment, the body may be modeled as a three-dimensional elastic continuum by breaking it into a large number of solid elements which fit together, and for which a model of the material may be solved for determining the stresses and strains in each element. The elements are typically tetrahedral, the nodes being the vertices of the tetrahedra (tetrahedralize a three dimensional region bounded by a polygon mesh into tetrahedra, similarly to how a two-dimensional polygon may be triangulated into triangles). The strain (which measures the local deformation of the points of the material from their rest state) may be quantified by the strain tensor. The stress (which measures the local forces per-unit area in all directions acting on the material) may be quantified by the Cauchy stress tensor. Given the current local strain, the local stress can be computed via the generalized form of Hooke's law. The equation of motion of the element nodes may be obtained by integrating the stress field over each element and relating this, via Newton's second law, to the node accelerations.

An energy minimization method can be used, which is motivated by variational principles and the physics of surfaces, which dictate that a constrained surface will assume the shape which minimizes the total energy of deformation (analogous to a soap bubble). Expressing the energy of a surface in terms of its local deformation (the energy is due to a combination of stretching and bending), the local force on the surface is given by differentiating the energy with respect to position, yielding an equation of motion which can be solved in the standard ways.

Shape matching can be used where penalty forces or constraints are applied to the model to drive it towards its original shape (e.g., the material behaves as if it has shape memory). To conserve momentum the rotation of the body must be estimated properly, for example via polar decomposition. To approximate finite element simulation, shape matching can be applied to three dimensional lattices and multiple shape matching constraints blended.

Deformation can also be handled by a traditional rigid-body physics engine, modeling the soft-body motion using a network of multiple rigid bodies connected by constraints, and using, for example, matrix-palette skinning to generate a surface mesh for rendering. This is the approach used for deformable objects in Havok Destruction.

The processes, computer readable medium and systems described herein may be performed on various types of hardware, such as computer systems 230. Such computer systems 230 may include a bus or other communication mechanism for communicating information and a processor coupled with the bus for processing information. A computer system 230 may have a main memory, such as a random access memory or other dynamic storage device, coupled to the bus. The main memory may be used to store instructions and temporary variables. The computer system 250 may also include a read-only memory or other static storage device coupled to the bus for storing static information and instructions.

The computer system 250 may also be coupled to a display, such as a CRT or LCD monitor 254. Input devices 256 may also be coupled to the computer system 250. These input devices 256 may include a mouse, a trackball, cursor direction keys, etc. for use by the user 258. Computer systems 250 described herein may include, but are not limited to, the computer 252, display 254, scanner/3D printer 260, and/or input devices 256. Each computer system 250 may be implemented using one or more physical computers or computer systems or portions thereof. The instructions executed by the computer system 250 may also be read in from a computer-readable medium. The computer-readable medium may be a CD, DVD, optical or magnetic disk, laserdisc, carrier wave, or any other medium that is readable by the computer system 250. In some embodiments, hardwired circuitry may be used in place of or in combination with software instructions executed by the processor.

As will be apparent, the features and attributes of the specific embodiments disclosed herein may be combined in different ways to form additional embodiments, all of which fall within the scope of the present disclosure.

Conditional language used herein, such as, among others, “can,” “could,” “might,” “may,” “e.g.,” and the like, unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain embodiments include, while other embodiments do not include, certain features, elements and/or states. Thus, such conditional language is not generally intended to imply that features, elements and/or states are in any way required for one or more embodiments or that one or more embodiments necessarily include logic for deciding, with or without author input or prompting, whether these features, elements and/or states are included or are to be performed in any particular embodiment.

Any process descriptions, elements, or blocks in the flow diagrams described herein and/or depicted in the attached figures should be understood as potentially representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process. Alternate implementations are included within the scope of the embodiments described herein in which elements or functions may be deleted, executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those skilled in the art.

All of the methods and processes described herein may be embodied in, and fully automated via, software code modules executed by one or more general purpose computers or processors, such as those computer systems described herein. The code modules may be stored in any type of computer-readable medium or other computer storage device. Some or all of the methods may alternatively be embodied in specialized computer hardware.

It should be emphasized that many variations and modifications may be made to the herein-described embodiments, the elements of which are to be understood as being among other acceptable examples. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.

The applications of the devices and methods discussed above are not limited to the one described but may include any number of further treatment applications. Modification of the above-described assemblies and methods for carrying out the invention, combinations between different variations as practicable, and variations of aspects of the invention that are obvious to those of skill in the art are intended to be within the scope of the claims. 

What is claimed is:
 1. A method for planning a treatment for correcting malocclusions, comprising: applying a label to one or more teeth within a digitized three-dimensional dental model; causing a simulated ball to roll digitally along an exterior of the one or more teeth and gums within the digitized three-dimensional dental model such that inflection changes in a path or trajectory of the simulated ball are detected, wherein the inflection changes are indicative of boundaries between each of the one or more teeth and gums; assigning a hard or soft region to each of the one or more teeth and gums within the digitized three-dimensional dental model; and moving a position of the one or more teeth within the digitized three-dimensional dental model to correct for malocclusions.
 2. The method of claim 1 wherein causing the simulated ball to roll digitally further comprises extrapolating a further boundary between adjacent teeth which is inaccessible to the simulated ball by projecting a trajectory of the simulated ball between the adjacent teeth.
 3. The method of claim 1 further comprising fabricating one or more aligners to move the one or more teeth according to the treatment.
 4. The method of claim 3 wherein fabricating one or more aligners comprises 3D printing the one or more aligners.
 5. The method of claim 1 wherein applying the label comprises receiving input from a user via a user interface in applying the label to the one or more teeth within the digitized three-dimensional dental model.
 6. The method of claim 1 wherein the inflection changes are further indicative of a crown/gum margin.
 7. The method of claim 1 wherein moving the position of the one or more teeth comprises applying a user-defined moving widget to the one or more teeth.
 8. The method of claim 7 wherein the moving widget comprises widgets for mesial/distal, lingual/facial, or vertical operations.
 9. The method of claim 1 wherein moving the position comprises morphing a new digitized three-dimensional dental model from the digitized three-dimensional dental model.
 10. The method of claim 9 wherein morphing comprises generating a model for a subsequent dental treatment stage.
 11. The method of claim 1 wherein each step occurs in a single visit by a subject to a dental office. 